2 Polarizers attenuating a light beam

[stefan3423]

Homework Statement

An angle is given between 2 polarizer's (45 degrees), through them light passes (unpolarized than after passing through the first one it polarizes), some of the light its shown on the display. For how much does the angle needs to be increased for the intensity of light to be 2 times less if the starting angle is 45 degrees.
Given Var:
α=45°

Homework Equations

I=I₀cos²α

The Attempt at a Solution

The answer in textbook:[/B]
α₂-α₁=+15°
My work:

My answer:(Side note I have a little error instead of II2 its I2, everything else is correct).

 

[kuruman]

Hi Stefan3423 and welcome to PF.

If the light intensity before going through the first polarizer is I₀, what is it after it passes through it?

 

[haruspex]

Homework Statement

An angle is given between 2 polarizer's (45 degrees), through them light passes (unpolarized than after passing through the first one it polarizes), some of the light its shown on the display. For how much does the angle needs to be increased for the intensity of light to be 2 times less if the starting angle is 45 degrees.
Given Var:
α=45°

Homework Equations

I=I₀cos²α

The Attempt at a Solution

The answer in textbook:[/B]
α₂-α₁=+15°
My work:View attachment 217015

The diagram is ok, but that is not really an attempt at a solution. Please show some thoughts at least.

 

[stefan3423]

The diagram is ok, but that is not really an attempt at a solution. Please show some thoughts at least.

Well I know that cos of 90 degrees=0 which means no light will go through the crystal and if cos of 0 degrees=1 i.e the crystal cross section will match thus max polarised light will pass through

 

[stefan3423]

Hi Stefan3423 and welcome to PF.

If the light intensity before going through the first polarizer is I₀, what is it after it passes through it?

Another polirised beam of light with max intensity but the secound poliriser is at angle of 45 degrees

 

[kuruman]

Another polirised beam of light with max intensity but the secound poliriser is at angle of 45 degrees

You did not answer my question. If the intensity of the beam is I₀ before the first polarizer, what is it after that polarizer? I am talking about the intensity between P1 and P2 in your drawing. There is no 45 degree angle involved, yet.

 

[stefan3423]

You did not answer my question. If the intensity of the beam is I₀ before the first polarizer, what is it after that polarizer? I am talking about the intensity between P1 and P2 in your drawing. There is no 45 degree angle involved, yet.

It starts with 45 degrees.BTW I solved it, found my errors and I will post my answer now.

 

[kuruman]

It starts with 45 degrees.BTW I solved it, found my errors and I will post my answer now.

Please do so.

 

[stefan3423]

You did not answer my question. If the intensity of the beam is I₀ before the first polarizer, what is it after that polarizer? I am talking about the intensity between P1 and P2 in your drawing. There is no 45 degree angle involved, yet.

 

[stefan3423]

Instead of II2 is I2=I1/2

 

[haruspex]

Looks good.

 

[jeremyfiennes]

Polarized light going through a filter at angle α emerges with intensity I₀cosα². A single photon going through the same filter has the same probability of being detected on the far side. Is this a general rule: intensity reduction factor = single photon detection probability? In which case, the Schroedinger function, where probability = amplitude², is a kind of "square root wave"?